58 citations · 373 across the 79 of their papers we have counts for
7 papers · 1 filter
On sums of Szemerédi--Trotter sets
Ilya D. Shkredov
We prove new general results on sumsets of sets having Szemerédi--Trotter type. This family includes convex sets, sets with small multiplicative doubling, images of sets under conv…
New sum-product type estimates over finite fields
Oliver Roche-Newton, Misha Rudnev, Ilya D. Shkredov
Let be a field with positive odd characteristic . We prove a variety of new sum-product type estimates over . They are derived from the theorem that the number of inciden…
Energies and structure of additive sets
Ilya D. Shkredov
In the paper we prove that any sumset or difference set has large E_3 energy. Also, we give a full description of families of sets having critical relations between some kind of en…
Additive dimension and a theorem of Sanders
Tomasz Schoen, Ilya D. Shkredov
We prove some new bounds for the size of the maximal dissociated subset of structured (having small sumset, large energy and so on) subsets A of an abelian group.
On Wiener norm of subsets of Z_p of medium size
Sergei V. Konyagin, Ilya D. Shkredov
We give a lower bound for Wiener norm of characteristic function of subsets A from Z_p, p is a prime number, in the situation when exp((log p/log log p)^{1/3}) \le |A| \le p/3.
Quantitative version of Beurling-Helson theorem
Sergei V. Konyagin, Ilya D. Shkredov
It is proved that any continuous function f on the unit circle such that the sequence e^{in f}, n=1,2,... has small Wiener norm \| e^{in f} \|_A = o (\frac{\log^{1/22} |n|}{(\log \…